(x+2.5)(x+2.5)=14.25

Solution for (x+2.5)(x+2.5)=14.25 equation:

(x+2.5)(x+2.5)=14.25

We move all terms to the left:

(x+2.5)(x+2.5)-(14.25)=0

We add all the numbers together, and all the variables

(x+2.5)(x+2.5)-14.25=0

We multiply parentheses ..

(+x^2+2.5x+2.5x+6.25)-14.25=0

We get rid of parentheses

x^2+2.5x+2.5x+6.25-14.25=0

We add all the numbers together, and all the variables

x^2+5x-8=0

a = 1; b = 5; c = -8;
Δ = b2-4ac
Δ = 52-4·1·(-8)
Δ = 57
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{57}}{2*1}=\frac{-5-\sqrt{57}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{57}}{2*1}=\frac{-5+\sqrt{57}}{2}
$